Stability and Frequency Compensation (Ch. 10) 김영석충북대학교전자정보대학 2010.3.1 Email: kimys@cbu.ac.kr 전자정보대학김영석 1
Basic Stability 10.1 General Considerations Y X (s) = H(s) 1+ βh(s) May oscillate at ω if βh(jω) =1 and βh( jω) = 180 (Barkhausen criteria) 전자정보대학김영석 2
Stable and Unstable Systems (a) 위상 =-180 도에서 Excessive Gain>1 => Unstable (b) 위상 =-180 도에서 Gain<1 => Stable 전자정보대학김영석 3
Stability and Complex Poles (a) Unstable with Growing Amplitude (b) Unstable with Constant Amplitude Oscillation (c) Stable σ σ σ p p p > 0 = 0 < 0 전자정보대학김영석 4
전자정보대학김영석 5 Basic One Pole Bode Plot βh =1 일때 Phase -180 도 (Barkhausen 조건 ) 만족못함 => Unconditionally Stable ) (1 1 1 ) ( 1 ) ( ) ( / 1 ) ( 0 0 0 0 0 0 A w s A A s H s H s X Y w s A s H β β β + + + = + = + =
Multipole Systems βh =1일때 Phase -180도에근접하면 Unstable Phase > -180도 => Stable H ( s) = (1 + s / w A 0 )(1 + s / p1 w p 2 ) 전자정보대학김영석 6
Phase Margin βh =1일때 (Phase+180)=Phase Margin Phase Margin ~ 0 => UnStable (a) 전자정보대학김영석 7
Phase Margin (cont.) Phase Margin=45도이상이필요함 Phase Margin=45도일때주파수 overshoot 30% Phase Margin, θ m = 45 전자정보대학김영석 8
Phase Margin (cont.) Phase Margin 증가하면 Time Domain Response 에서 Ringing 감소 (Freq Domain Response에서 Peaking 감소 ) 전자정보대학김영석 9
Small Signal Analysis Limitations 다음회로의경우 Bode Plot(Small Signal Analysis) 에서 PM=60 도임. 그러나 Large Signal Analysis 에서는 Ringing 을보임. 그이유로 Slewing, 소자의 Nonlinear Behavior 때문임. Large Signal Application 의경우이와같은 Time Domain 해석이필요함 Small signal analysis yields 65 of θ m, but large signal transient response is different. Large signal simulation includes effects not seen in small signal analysis. 전자정보대학김영석 10
10.4 Frequency Compensation Unstable System 을 Stable 하게하기위해서 Freq. Comp. 필요함 Compensation is the manipulation of gain and/or pole positions to improve phase margin. 전자정보대학김영석 11
Compensation (cont.) Dominant Pole 을 Low Freq 로옮김 => PM 확보 전자정보대학김영석 12
Single Ended Single Stage Amp Dominant Pole=Wout: Large CL/Rout A Node: Large Stray Cap. => 2 nd Dominant Pole 전자정보대학김영석 13
Single Ended Single Stage Amp (cont) Pre- and Post-Compensation PM 없음 => Unstable Freq Comp: Dominant Output Pole을낮은주파수로이동시킴. 다른 Pole 들은그대로둠. => PM 45도확보 전자정보대학김영석 14
Fully Differential Telescopic Op-Amp No Mirror Pole => Bandwidth 증가 전자정보대학김영석 15
10.5 Comp. of Two Stage Op AMps Wp,x: 높은주파수 Wp,E: Large R => 낮은주파수 Wp,A: R=ro, Large CL=> 낮은주파수 Unstable 전자정보대학김영석 16
Compensation (cont.) Miller Compensation Miller Cap Cc로 E Node의 Dominant Pole을낮은주파수로이동 Miller Effect C eq = C E + (1 + A v 2 )C C f pe = 1 2πR out [C E + (1 + A v 2 )C C ] 전자정보대학김영석 17
fp,in = Wp,E/2/pi => 작아짐 Compensation (cont.) Recall, from Chap. 6: (assume C C includes C GD9 ) 1 f p,in = 2π R S [ C E + (1+ g m R L )C C ]+ R L (C C + C L ) ( ) f p,in 2πR S 1 [ ] C E + (1+ g m R L )C C 전자정보대학김영석 18
fp,out = Wp,A/2/pi => 커짐 Compensation (cont.) f p,out = R S (1 + g m 9 R L )C C + R S C E + R L (C C + C L ) 2πR S R L (C E C C + C E C L + C C C L ) f p,out R S g m 9 R L C C + R L C C 2πR S R L (C E C C + C C C L ) = g m 9 2π(C E + C L ) 전자정보대학김영석 19
Compensation (cont.) 앞의 Compensation 은 RHP zero 발생 => Phase margin 악화시킴 Recall, transfer function includes (1 s/ω z ) numerator term and f Z (RHP) = g m9 2πC C 전자정보대학김영석 20
Phase and Magnitude of RHP Zero 전자정보대학김영석 21
RHP zero 제거위해 Rz 저항삽입 RHP Zero Removal f Z = g m 9 2πC C (1 /g m 9 R Z ) 전자정보대학김영석 22
RHP Zero Removal (cont.) f Z = 1 2πC C (1/ g m 9 R Z ) Could set R z =1/g m9, or cancel other non- dominant pole 1 C C (1 /g m 9 R Z ) = R Z = C L + C E + C C g m 9 C C g m9 C L + C E C L + C C g m 9 C C = w p,a 전자정보대학김영석 23
Miller Compensation (cont.) V V R = GS13 GS15 on15 1 g m9 = VGS9되게 I 1 조절 = VGS14 1 = μ C ( W / L) ΔV p C (1 + C ox L C 15 15 )(Pole Zero = 1 ( W g ( W m14 / L) / L) 14 15 Cancellation) Temp. and Process Tracking 전자정보대학김영석 24
Miller Compensation (cont.) Defining gm9 with respect to Rs 전자정보대학김영석 25
Load Capacitance Effects One Stage: Increase CL => Increase PM => More Stable Two Stage: Increase CL => Output Pole 을낮은주파수로이동시킴. Cc 에의한 1 st Stage Output Pole(Dominant) 쯕으로이동시켜 PM 을악화시킴 전자정보대학김영석 26
10.6 Other Compensation Techniques 전자정보대학김영석 27
Other Compensation Techniques (cont.) f p1 1 2πR S g m1 R L C C f p2 g m1 2πC L 전자정보대학김영석 28
Other Compensation Techniques (cont.) 전자정보대학김영석 29
Other Compensation Techniques (cont.) f p1 1 2πR S g m1 R L C C f p2 g m1g m 2 R S 2πC L 전자정보대학김영석 30
Slewing in Two-Stage Op Amps Basic Two-Stage Op Amp 전자정보대학김영석 31
Slewing in Two-Stage Op Amp 전자정보대학김영석 32
Slewing with Common-Gate Compensation 전자정보대학김영석 33